Question

Prove that external angle is sum of the opposite interior angle.

Answer 1

For line $QS$

$\angle 3+\angle 4=180°$ [linear pair] $⟶\left(1\right)$

In $△PQR$

$\angle 1+\angle 2+\angle 3=180°$ [Angle property of triangle ] $⟶\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$\angle 3+\angle 4=\angle 1+\angle 2+\angle 3=180°$

$\angle 4=\angle 1+\angle 2$

$\angle PRS=\angle RPQ+\angle PQR$

Hence, exterior angle is sum of two appoints interior angle.